面向对称矩阵变量数据的贝叶斯高斯混合建模
Bayesian Gaussian Mixture Modeling for Symmetric Matrix Variate Data
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中文总结 AI 辅助
针对个体活动网络统计推断难题，提出STRUCTURED模型及其两个变体，经模拟和金县293人GPS数据验证，STRUCTURED-RJ适用于稀疏数据、STRUCTURED-FP适用于大样本，可揭示影响活动重叠模式的人口统计因素。
中文摘要 AI 辅助
由于缺乏合适粒度的可用数据以及个体移动模式建模的复杂性，对个体活动网络进行统计推断历来是一项艰巨任务。近期，来自个体设备的GPS数据与高度详细的人口统计信息的可获得性表明，其中一项挑战如今可得到解决。我们引入了一种名为对称矩阵变量正态混合模型（STRUCTURED）的新模型，用于估计人口统计特征如何影响人类活动网络的变化，该模型利用了随时间捕获个体间概率空间重叠的社会矩阵。我们利用对称矩阵变量正态分布固有的交换性约束，将列精度矩阵参数化为行精度矩阵的多项式，从而将有效参数空间减少一个数量级。我们开发了STRUCTURED的两个变体：用于估计完整多项式的STRUCTURED-FP，以及使用可逆跳转MCMC选择降阶参数化的STRUCTURED-RJ。模拟研究表明，在稀疏数据场景下，STRUCTURED-RJ的性能优于现有方法；而当样本量较大时，STRUCTURED-FP更受青睐。我们将该模型应用于美国华盛顿州金县293名个体的GPS衍生社会矩阵，发现本地犯罪环境与青年就业密度是解释每周活动重叠模式变化的主要人口统计因素。
英文摘要
Statistical inference on individual activity networks has been a historically difficult task due to the lack of available data at the appropriate granularity and the complexity of modeling individual mobility patterns. The recent availability of GPS data from individual devices, combined with highly detailed demographic information, suggests that one of these challenges can now be addressed. We introduce a new model which we call the Symmetric Matrix-Variate Normal Mixture Model (STRUCTURED) to estimate how demographic traits influence changes in human activity networks, using sociomatrices that capture the probabilistic spatial overlap between individuals over time. We exploit the commutativity constraint inherent in the symmetric matrix-variate normal distribution to parameterize the column precision matrix as a polynomial of the row precision matrix, reducing the effective parameter space by an order of magnitude. We develop two variants of STRUCTURED: STRUCTURED-FP, which estimates the full polynomial, and STRUCTURED-RJ, which uses reversible-jump MCMC to select a reduced-order parameterization. Simulation studies demonstrate that STRUCTURED-RJ outperforms existing methods in sparse-data regimes, whereas STRUCTURED-FP is preferred when sample sizes are large. We apply the model to GPS-derived sociomatrices of 293 individuals in King County, WA, finding that local crime environments and youth employment density are the dominant demographic factors explaining variation in weekly activity overlap patterns.
